You may pause call recording from the Agent Desktop. When enabled, the recording controls will show on the Agent Desktop screen while you are "In Call' status.
While "In Call" status, you will see the resume (play), pause and stop buttons as shown below.

Depending on the configuration, you may just see pause and resume (play) button. 

The recording is turned on automatically upon connecting to the call. If call ends with call recording paused, the recorder will automatically re-initiate on the next call.